- 9.2.31E: State the null and alternative hypothesis in each case.(a) A hypoth...
- 9.2.32E: A hypothesis will be used to test that a population mean equals 7 a...
- 9.2.33E: A hypothesis will be used to test that a population mean equals 10 ...
- 9.2.34E: A hypothesis will be used to test that a population mean equals 5 a...
- 9.2.35E: For the hypothesis test and variance known, calculate theP-value fo...
- 9.2.36E: For the hypothesis test and variance known, calculate the P-value f...
- 9.2.37E: For the hypothesis test variance known, calculate the P-value for e...
- 9.2.38E: Output from a software package follows:
- 9.2.39E: Output from a software package follows:
- 9.2.40E: Output from a software package follows:
- 9.2.41E: Output from a software package follows:
- 9.2.42E: The mean water temperature downstream from a discharge pipe at a po...
- 9.2.43E: A manufacturer produces crankshafts for an automobile engine. The c...
- 9.2.44E: A melting point test of n = 10 samples of a binder used in manufact...
- 9.2.45E: The life in hours of a battery is known to be approximately normall...
- 9.2.46E: An engineer who is studying the tensile strength of a steel alloy i...
- 9.2.47E: Supercavitation is a propulsion technology for undersea vehicles th...
- 9.2.48E: bearing used in an automotive application is supposed to have a nom...
- 9.2.49E: Medical researchers have developed a new artificial heart construct...
- 9.2.50E: Humans are known to have a mean gestation period of 280 days (from ...
- 9.2.51E: The bacterial strain Acinetobacter has been tested for its adhesion...
Solutions for Chapter 9.2: Applied Statistics and Probability for Engineers 6th Edition
Full solutions for Applied Statistics and Probability for Engineers | 6th Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Another name for factors that are arranged in a factorial experiment.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Discrete random variable
A random variable with a inite (or countably ininite) range.
A subset of a sample space.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
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